References
[BB] F. Bethuel and H. Brezis Minimisation de\(\int | \nabla (u - \tfrac{x}{{\left| x \right|}})|^2 \) dx et divers phénomènes de gap, C. R. Acad. Sci. Paris310 (1990), 859–864
[BC1] H. Brezis, J. M. Coron,Multiple solutions of H-systems and Rellich's conjecture, Commun. Pure Appl. Math.37 (1984), 149–187
[BC2] H. Brezis, J. M. Coron,Large solutions for harmonic maps in two dimensions, Commun. Math. Phys.92 (1983), 203–215
[EL] J. Eells, L. Lemaire,Another report on Harmonic maps, Bull. London Math. Soc.20 (1988), 385–524
[F] A. Friedman,Partial differential equations, Holt, Rimehart and Winston. Inc. (1969)
[GH] B. Guo, M.-C. Hong,The Landau-Lifshitz equation of the ferromagnetic spin chain and harmonic maps, Calc. Var.1 (1993) 311–334
[HZ] R. Hadiji, F. Zhou, Regularity of\(\smallint _\Omega \left| {\nabla u} \right|^2 + \lambda \left| {u - f} \right|^2 \) and some gap phenomenon, to appear
[He] F. Helein,Regularity of weak harmonic maps from a surface into a manifold with symmetries, Manuscripta Math.70 (1991), 203–218
[HKW] S. Hildebrandt, H. Kaul, K.-O. Widman,An existence theorem for harmonic mappings of Riemannian manifolds, Acta Math.138 (1977), 1–16
[Ho] M.-C. Hong,The Landau-Lifshitz equation with the external field—A new extension for harmonic maps with value intoS2,Math. Z. (to appear)
[KW] H. Karcher, J. C. Wood,Non-existence results and growth properties for harmonic maps and forms, J. Reine Angew. Math.353 (1984), 165–180
[J] J. Jost,The Dirichlet problem for harmonic maps from a surface with boundary onto a 2-sphere with nonconstant boundary values, J. Diff. Geom.19 (1984), 393–401
[LU] O. A. Ladyzenskaja, N. N., Ural'ceva,Linear and quasilinear elliptic equations, Academic Press, New York and London (1968)
[L] L. Lemaire,Applications harmoniques de surfaces Riemanniennes, J: Diff. Geom.13 (1978), 51–78
[M] C. B. Morrey,Multiple integrals in the calculus of variations, Grundlehren 130, Springer, Berlin (1966)
[W1] H. Wente,The Dirichlet problem with a volume constrain, Manuscripta Math.11 (1974), 141–157
[W2] H. Wente,An existence theorem for surface of constant mean curvature, J. Math. Anal. Appl.26 (1969), 318–344
[Wo] J. C. Wood,Non existence of solutions to certain Dirichlet problems for harmonic maps I, Preprint, Leeds, (1981)
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Hong, MC., Lemaire, L. Multiple solutions of the static landau-lifshitz equation fromB 2 intoS 2 . Math Z 220, 295–306 (1995). https://doi.org/10.1007/BF02572616
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DOI: https://doi.org/10.1007/BF02572616